A-LevelMathematicsProbability and statistics9709/61 · May/June 2017 · Q57 Marks
Eggs are sold in boxes of 20. Cracked eggs occur independently and the mean number of cracked eggs in a box is 1.4.
- (i)Calculate the probability that a randomly chosen box contains exactly 2 cracked eggs.[3]
- (ii)Calculate the probability that a randomly chosen box contains at least 1 cracked egg.[2]
- (iii)A shop sells n of these boxes of eggs. Find the smallest value of n such that the probability of there being at least 1 cracked egg in each box sold is less than 0.01.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- [B1] p = 0.07
- [M1] Bin term 20Cxp^x (1-p)^(20-x) their p
- [A1]
- [M1] Attempt to find P(at least1 cracked egg) with their p from (i) allow 1 – P(0, 1) OE
- [A1] Rounding to 0.766
- [M1] Eqn or inequal containing (their 0.766)^n or (their 0.234)^n, together with 0.01 or 0.99
- [A1]
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